Analyzing quantum entanglement with the Schmidt decomposition in operator space

TL;DR

This paper introduces a new method for constructing entanglement witnesses using the Schmidt decomposition of observables, applicable to many-body systems, and demonstrates improved entanglement detection in experiments.

Contribution

A novel approach to entanglement witness construction based on Schmidt decomposition, surpassing fidelity-based methods and applicable to complex quantum systems.

Findings

Method works for many-body systems

Improves entanglement detection accuracy

Can quantify and characterize entanglement dimensionality

Abstract

Characterizing entanglement is central for quantum information science. Special observables which indicate entanglement, so-called entanglement witnesses, are a widely used tool for this task. The construction of these witnesses typically relies on the observation that quantum states with a high fidelity to some entangled target state are entangled, too. We introduce a general method to construct entanglement witnesses based on the Schmidt decomposition of observables. The method works for two- and, more importantly, many-body systems and is strictly stronger than fidelity-based constructions. The resulting witnesses can also be used to quantify entanglement as well as to characterize the dimensionality of it. Finally, we present experimentally relevant examples, where our approach improves entanglement detection significantly.